Python Math: Convert a floating point number to an approximate rational value

Last update on April 24 2025 12:44:25 (UTC/GMT +8 hours)

47. Approximate PI as a Fraction

Write a Python program to convert a floating point number (PI) to an approximate rational value on the various denominators.

Note: max_denominator = 1000000

Sample Solution:

Python Code:

import fractions
import math

print('PI       =', math.pi)

f_pi = fractions.Fraction(str(math.pi))
print('No limit =', f_pi)

for d in [1, 5,  50, 90, 100, 500, 1000000]:
    limited = f_pi.limit_denominator(d)
    print('{0:8} = {1}'.format(d, limited))

Sample Output:

PI       = 3.141592653589793                                                                                
No limit = 3141592653589793/1000000000000000                                                                
       1 = 3                                                                                                
       5 = 16/5                                                                                             
      50 = 22/7                                                                                             
      90 = 267/85                                                                                           
     100 = 311/99                                                                                           
     500 = 355/113                                                                                          
 1000000 = 3126535/995207

Flowchart:

$Flowchart: Convert a floating point number to an approximate rational value$

For more Practice: Solve these Related Problems:

Write a Python program to convert the value of PI to a Fraction using a given maximum denominator and print the resulting approximation.
Write a Python function that accepts a maximum denominator, approximates PI as a Fraction, and returns the numerator and denominator.
Write a Python script to compute several rational approximations of PI with different maximum denominators and display them side by side.
Write a Python program to compare the Fraction approximation of PI with the built-in math.pi and print the absolute difference.

Go to:

Previous: Write a Python program to add, subtract, multiply and divide two fractions.
Next: Write a Python program to generate random float numbers in a specific numerical range.

Python Code Editor:

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